\section{Integrate And Fire}
\label{sec:IntegrateAndFire}

\subsection{Design}

The Integrate And Fire circuit uses a Simple Transconductance Amplifier (Listing ~\ref{lst:STA}) with $G_m = 250nS$ and $R_{out}=1G\Ohm$. Several parameters were left as variables to be changed during various experiments. These parameters are described in Table~\ref{tbl:IAF_parameters}.

\begin{table}[H] \centering
		\begin{tabular}{ccc}
			Parameter & Description & Default Value \\ \hline  
			$C_f$ & Feedback Capacitance &  $100fF$ \\   
			$I_{in}$ & Input Current &  $1nA$ \\   
			$W_{inv,p1}$ & Width of pFET of the first inverter &  $1.5\mu m$ \\  
		\end{tabular}
		\caption{Parameters left as variables in the Integrate And Fire circuit.}
		\label{tbl:IAF_parameters}
\end{table}

\begin{figure}[H] \centering
\includegraphics[width=\columnwidth]{../Data/IntegrateAndFire_sch.png}
\caption{\label{fig:IAF_schematic} Schematic for an Integrate And Fire.}
\end{figure}

\subsection{Testing}

The variables in Table \ref{tbl:IAF_parameters} are varied to study the behavior of the circuit.

\begin{figure}[H] \centering
\includegraphics[width=\columnwidth]{../Data/IntegrateAndFire_1nA_DefaultSize_Full.png}
\caption{\label{fig:IAF_cf} Results for transient simulation of the Integrate and Fire with changing feedback capacitance.}
\end{figure}


\begin{figure}[H]
\begin{center}
\begin{tabular}{c}
	\includegraphics[width=\columnwidth]{../Data/IntegrateAndFire_100pA_DefaultSize_Full.png} \\	
	\includegraphics[width=\columnwidth]{../Data/IntegrateAndFire_100pA_DefaultSize_Zoom.png} \\	
\end{tabular}
\end{center}
\vspace*{-0.2cm}
\caption{Results for transient simulation of the Integrate and Fire with $.1nA$ input current. (a) Full View (b) Zoomed View}
\label{fig:IAF_Iin}
\end{figure}

\begin{figure}[H] \centering
\includegraphics[width=\columnwidth]{../Data/IntegrateAndFire_1nA_Full.png}
\caption{\label{fig:IAF_WpFET} Results for transient simulation of the Integrate and Fire with different thresholds.}
\end{figure}


\subsection{Evaluation}

The circuit behavior can be characterized by three characteristics:

\begin{enumerate}
	\item $t_{H}$ $\frac{C_f V_{dd}}{I_r - I_{in}}$ - Amount of time that the output pulse stays high after a "`fire"'
	\item $t_{L}$ $\frac{C_f V_{dd}}{I_{in}}$ - Amount of time that the output pulse stays low while "`recharging"'
	\item $\Delta V_{mem}$ $\frac{C_f V_{dd}}{C_f + C_m}$ - The amount of change in $V_{mem}$ as the circuit "`fires"'
\end{enumerate} 

\begin{table}[H] \centering
		\begin{tabular}{c|ccccc|ccc}
			Simulation & $t_{H}$ & $t_{L}$ & $\Delta V_{mem}$ \\ \hline 
			(a) $C_f = 10fF$ & $92.300ns$ & $51.252\mu s$ & $79.666mV$ \\
			(b) $C_f = 255fF$ & $4.896\mu s$ & $0.291ms$ & $1.598V$ \\
			(c) $C_f = 500fF$ & $4.896\mu s$ & $2.147ms$ & $2.333V$ \\
		\end{tabular}
		\caption{Results for the evaluation of the Integrate And Fire circuit with varying parameters.}
		\label{tbl:IAF_charac_results}
\end{table}